The Duration of Trade Revisited: Continuous-Time vs. Discrete-Time Hazards

Abstract

The recent literature on the duration of trade has predominantly analyzed the determinants of trade flow durations using Cox proportional hazards models. The purpose of this paper is to show why it is inappropriate to analyze the duration of trade with continuous-time models such as the Cox model, and to propose alternative discrete-time models which are more suitable for estimation. Briefly, the Cox model has three major drawbacks when applied to large trade data sets. First, it faces problems in the presence of many tied duration times, leading to biased coefficient estimates and standard errors. Second, it is difficult to properly control for unobserved heterogeneity, which can result in spurious duration dependence and parameter bias. Third, the Cox model imposes the restrictive and empirically questionable assumption of proportional hazards. By contrast, with discrete-time models there is no problem handling ties; unobserved heterogeneity can be controlled for without difficulty; and the restrictive proportional hazards assumption can easily be bypassed. By replicating an influential study by Besedes and Prusa from 2006, but employing discrete-time models as well as the original Cox model, we find empirical support for each of these arguments against the Cox model. Moreover, when comparing estimation results obtained from a Cox model and our preferred discrete-time specification, we find significant differences in both the predicted hazard rates and the estimated effects of explanatory variables on the hazard. In other words, the choice between models affects the conclusions that can be drawn.